INVESTIGATION OF AEROSOLS SPREADING CONDITIONS IN ATMOSPHERE
USING REMOTE SENSING DATA AND NON–HYDROSTATIC METEOROLOGICAL
NUMERICAL MODELS DATA
I. A. Winnicki * , K. Kroszczynski, J. M. Jasinski, S. Pietrek
Faculty of Civil Engineering and Geodesy, Military University of Technology Kaliskiego 2 Str., 00–908 Warsaw,
Poland -(ireneusz.winnicki@wat.edu.pl, janusz.jasinski@wat.edu.pl, rwkk@.op.pl, spietrek@wat.edu.pl)
Commission VIII, WG VIII/3
KEY WORDS: Satellite remote sensing, Modelling, Image understanding, Simulation, Air Pollution, Prediction.
ABSTRACT:
Two ways of aerosols spreading analysis in atmosphere are presented. The first one is based on the one–level barotropic models.
This case includes the simple tests of the numerical simulations spreading of a clouds of contaminants in free atmosphere. The
solutions for this example was obtained using the non–divergent equation of the quasi–solenoidal or quasi–geostrophic models in the
barotropic approaches. The considered equation is a nonlinear differential equation of Monge–Ampere (MA) type used for
determining a streamfunction field when the geopotential field is known. It is obtained by transforming the governing equations and
assuming that the divergence of wind field is equal to zero. The nonlinear balance equation is a part of the general system equations
describing quasi–solenoidal or quasi–geostrophic models. The second way of the analysis is based on the COAMPS (Coupled
Ocean/Atmosphere Mesoscale Prediction System) non–hydrostatic numerical weather prediction model developed by Naval
Research Laboratory, Monterey, California (Hodur, 1997). This multi–level numerical weather forecasting model is tested in the
Applied Geomatics Section, MUT. Research results are presented to and discussed with students of geoinformatics and meteorology.
Weather forecast for Poland is presented every day on the Faculty’s web–page. The main equation describing the propagation
process – the aerosol–tracer continuity equation is derived from the mass flux form of the conservation equation. This form of the
continuity equation conserves the mass. In COAMPS, the 3D continuity equation is integrated forward in time with three equivalent
one–dimensional equations (time splitting method). Both the explicit and implicit numerical methods for integration in time are
available to solve the diffusion expressions in the continuity equation. The COAMPS nested grid model run on the IA64x32 Feniks
cluster with the three–dimensional aerosol–tracer module. This model is executed in Poland in order to recognize the distribution of
tropospheric aerosol and chemical conditions for the first time. The Mazovian Province digital terrain model (DTM) is taken into
consideration. In this case the simulations of the propagation of gas pollution emitted by the four Warsaw Power Plant chimneys:
Wola, Kaweczyn, Siekierki and Zeran are presented. The chosen analysis also include the pollution from the Steelworks Warsaw
(west part of the capitol).
solenoidal model) treating the geopotential as known data –
solution of the balance equation.
2. Predicting of the geopotential field (quasi–geostrophic
model) or the streamfunction field (the quasi–solenoidal
model) for 12 or 24 hours, for instance, and
3. Solving the balance equation for geopotential or
streamfunction. In the quasi–geostrophic model, on the
basis of the prognostic geopotential field, we obtain a
prognostic wind field. In the quasi–solenoidal model, on the
basis of prognostic streamfunction we obtain a prognostic
geopotential field.
1. INTRODUCTION
On the base of real measurement data (geopotential of the
isobaric 500 hPa surface) obtained from the GRID data sets the
barotropic model in quasi–solenoidal approach is solved. The
method of analysis of the point–source gas pollutant
propagation in the barotropic atmosphere is presented. The
wind components are defined as a streamfunction. Solutions of
some numerical simulations are presented. The nonlinear
balance equation is a part of the general system equations
describing quasi–solenoidal or quasi–geostrophic models.
For the realization of the first stage of the weather forecasting
process it is necessary to analyze a non–linear balance equation
for streamfunction ψ, a particular case of Monge–Ampere (MA)
equation type. It is a diagnostic equation. Because of the
nonlinearity, an iterative solution procedure must be used. The
main point is that if it lead to a convergent sequence of solution
they have to satisfy the general condition of a convergence of
the Monge–Ampere equation. That condition depends mostly
on the geometry of the geopotential field. The curvature of this
field must be elliptic. It is an ellipticity criterion of the balance
equation. Let us consider a system of barotropic primitive
2. PRIMITIVE EQUATIONS AND DIFFUSION
2.1 Primitive Equations
The numerical weather forecasting process based upon the non–
divergent models in barotropic approaches can be divided into
three following stages:
1. Computing the horizontal components of the wind velocity
(the geostrophic model) or the stream–function field (the
*
Corresponding author.
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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B8. Beijing 2008
q = ∂ψ / ∂t – the streamfunction tendency,
α 2 = f /ψ – parameter.
With respect to q (8) is Helmholtz equation. Meteorologists call
it barotropic divergent model in quasi–solenoidal approach or
generalized vorticity equation. In Figure 1 the contour plots of
500 hPa height data (input geopotential data) obtained from the
meteorological measurements are shown. In Figure2 the contour
plots of wind velocity for the analysed geopotential field is
illustrated.
equations, known as the shallow water model. It can be written
in Cartesian coordinates:
∂Φ
∂u
∂u
∂u
+ fv
=−
+v
+u
∂x
∂y
∂x
∂t
∂v
∂v
∂v
∂Φ
+u +v = −
− fu
∂t
∂y
∂y
∂y
⎛ ∂u ∂v ⎞
∂Φ
∂Φ
∂Φ
+ Φ⎜⎜ + ⎟⎟ = 0
+v
+u
∂y
∂x
∂t
⎝ ∂x ∂y ⎠
where:
where:
(1)
Φ = gH – geopotential, (H – the free surface
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Figure 1. Input geopotential Φ field (measured data).
(3)
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Let us turn the attention to the real atmospheric motions. They
usually consist small perturbations. One can describe them as:
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M
N
∑∑ψ ij
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The Monge–Ampere equation is a second order nonlinear
partial differential one, which can be written in general form
r ⋅ t − s 2 = a ⋅ r + 2b ⋅ s + c ⋅ t + ϑ
(9)
(6)
where:
where:
M, N – number of grid points along x and y axes.
Finally we obtain
r=
∂ 2ψ
∂x 2
s=
∂ 2ψ
∂x∂y
t=
∂ 2ψ
∂y 2
(10)
Its coefficients a, b and c depend on x, y, the sought–for
function and its first derivatives
(7)
or
p=
∇ 2 q − α 2 q = J (∇ 2ψ + f ,ψ )
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2.2 The Balance Equation
i =1 j =1
f ∂ψ
∂∇ 2ψ
−
J (∇ 2ψ + f ,ψ ) = 0
∂t
ψ ∂t
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9 12 15
Figure 2. Wind velocity field of the 500 hPa level.
(5)
For the sake of simplicity it is suggested to treat the
streamfunction ψ in the denominator of the coefficient at the
time derivative as a constant value being the mean value over
the considered area. Hence
1
ψ =
M ⋅N
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Substituting (4) for (2) and neglecting the terms of lower order
one can obtain:
f ∂ψ
∂∇ 2ψ
−
J (∇ 2ψ + f ,ψ ) = 0
∂t
ψ ∂t
9
9
18
u’, v’ – fluctuations in the x and y directions.
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where:
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(4)
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∂ψ
∂ψ
+ u ' v = vψ + v ' =
+ v'
∂y
∂x
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u = uψ + u ' = −
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where streamfunction ψ is defined by the relations:
∂ψ
∂x
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⎛ ∂u ∂v ⎞ (2)
∂∇ 2ψ
∂ (∇ 2ψ + f )
∂ (∇ 2ψ + f )
+u
+v
= −(∇ 2ψ + f )⎜⎜ + ⎟⎟
∂x
∂y
∂t
⎝ ∂x ∂ y ⎠
vψ =
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This transformation leads to the vorticity equation for ∇ 2ψ :
∂ψ
∂y
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height),
u, v – are the components of the wind vector
along the x and y axes of the coordinate
Cartesian system,
g – gravity acceleration,
f – Coriolis parameter, f = 2ω sin ϕ ,
φ – latitude.
uψ = −
Geopotential: 500 hPa
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∂ψ
∂x
q=
∂ψ
∂y
(8)
where:
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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B8. Beijing 2008
Let us present the final form of the balance equation as
∂ ψ ∂ ψ ⎛ ∂ ψ
⋅
−⎜
∂ x 2 ∂ y 2 ⎜⎝ ∂x ∂y
2
2
2
2
2.4 Numerical simulations
Note: The choice of sources localization was accidental. It was
strictly connected with geopotential and wind fields over the
Europe and North Atlantic, which were included into
considerations. For the calculations the first source was placed
at the start of the convergence zone over the Atlantic Ocean, the
second – at its end (North Africa).
⎞
∂ ψ
∂ ψ
∂ ψ
⎟⎟ + a ⋅
+ 2b ⋅
+c⋅
+ϑ = 0
2
∂
∂
∂
∂y 2
x
x
y
⎠
2
2
2
(11)
where:
a=c=
f
2
b=0
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2
1 ⎛ ∂ψ ∂ f ∂ψ ∂ f ⎞
⎟
+
2 ⎝ ∂x ∂x ∂y ∂y ⎟⎠
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ϑ = − ∇2Φ + ⎜⎜
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Solving the balance equation for streamfunction we obtain the
prognostic wind field and next one can solve the advection –
diffusion two – dimensional problem (red closed lines in the
Figure 3 through Figure 5).
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The MA equation may be of elliptic, hyperbolic or parabolic
type. The type depends on the sign of expression
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Δ = (2 ⋅ ∇ Φ = f ) / 4
2
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(12)
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Emission rate:
which is called an ellipticity criterion for MA equation. If Δ > 0
the MA equation is of elliptic type. In the opposite case it is
hyperbolic and if Δ = 0 the MA equation is of parabolic type.
The solution of the equation (11) is physically acceptable only
when it is of elliptic type (Winnicki, 1995).
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Forecast:
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Figure 3. Simulation after 6 hours.
The criterion (12) depends strongly on the sign of ∇2Φ and
relations between the geopotential field and Coriolis parameter f.
In the real atmosphere the condition of ellipticity
Δ = 2 ⋅ ∇ 2 Φ = f 2 / 4 > 0 is usually satisfied in the high and
mid-latitudes for majority atmospheric situations, including
anticyclones and atmospheric fronts. In spite of the ∇2Φ < 0,
the criterion 2 ⋅ ∇ 2Φ + f 2 > 0 is true. In the area of low
(
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pressure (cyclones) due to the relation ∇2Φ > 0 the ellipticity
condition is always satisfied. It does not depend on the latitude.
For low latitudes criterion (12) is not satisfied for anticyclones
with high anticyclonic curvature and the modification of
geopotential field is obligatory. The function f2 reaches 0 very
fast. The observation data sometimes need to be modified to
satisfy the ellipticity criterion of the balance equation.
Two point–sources (e.g. nuclear plants) are located in the
considered area. Its coordinates are (66oN, 20oW) – Iceland and
(30oN, 6oW) – Morocco. The stars show their positions. The
first source of pollution there is in the area of very strong wind
(see Figure 2). Considered plant is located on the edge of the
convergence zone. The propagation process runs very fast. The
range of contamination is growing to the south of the Atlantic
Ocean reaching the south part of the Spain and Morocco (see
Figure 3 through Figure 5).
The second plant is located at the edge of the divergence zone.
The propagation process runs slower. The range of
contamination does not grow so fast.
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2.3 Advection – Diffusion Equation for the Quasi–
Solenoidal Approach
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The diffusion equation with advection terms solved here can be
written as follows
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⎛∂ C ∂ C⎞
∂C
∂C
∂C
+u
+v
− K xy ⎜⎜ 2 + 2 ⎟⎟ = Q( x, y, t )
∂t
∂x
∂y
∂y ⎠
⎝ ∂x
2
2
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(13)
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where:
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C – concentration of the gas pollutant,
Kxy – the kinematics coefficients of eddy
viscosity for horizontal eddies,
Q(x,y,t) – the point–source gas pollutant
emission rate (mass per unit time).
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Figure 4. Simulation after 12 hours.
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the nested grid.
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Figure 5. Simulation after 36 hours.
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0
500
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Figure 6. Telescopic multi-nested calculation grid
3. THE COAMPS AEROSOL–TRACER MODULE
3.1 Introduction
The increasing level of atmosphere pollution caused by the
development of industry, mass-production, transportation,
extraction of resources and influence of urban areas affects
greatly the natural environment. During the previous century
the natural environment was subject to a vast change. The
greenhouse effect, ozone hole, acid rain, decrease in forest areas,
electromagnetic smog, are only a part of the present ecological
threats caused by human. This is why conducting research
studies concerning the emission and propagation of gas
pollution is vital. The Ministry of the Environment decree
(dated 13 June 2003), concerning the measuring of emission
levels, defines the official requirements regarding the
continuous measurements of gaseous pollutant emission levels,
which must be conducted above all by heat and power plants,
steelworks and plants emitting air organic pollutants. The
Directive 2001/81/WE of the European Parliament and of the
Council (dated 23 October 2001) makes it obligatory for all the
EU nations to reduce by 2010 their annual emission of sulfur
dioxide, nitrous oxides, gaseous organic compounds and
ammonia to the levels defined in the Directive. The research
conducted by Applied Geomatics Section concern the
distribution of gases (CO2, N2O, NOx, SO2, H2S, aromatic
compounds), aerosols and dusts (radioactive wastes), which
constitute the main source of pollution.
The future studies including the introduction of more advanced
parameterization of the COAMPS model (i.e. adjusted
numerical model or modified algorithm of the turbulence and
planetary boundary layer) will cover also the pollution caused
by ground vehicle transportation, chemical industry and
dispersed energy sources (NOx, SO2, dusts).
The COAMPS model is not here described precisely (for more
details see Hodur, 1997). COAMPS runs on the nested grid
methodology. Nested grid methodology (Figure 6) is used in
parallelized calculation process. This process is designed to
facilitate two way interaction in which the boundary and initial
conditions and state parameters, including pollution
concentration, may flow from the grid with large spatial step to
the sub-grid. It is possible also that the smaller scale processes
may affect the pollution propagation in the larger areas.
3.2 The Continuity Equation
The continuity equation written in the conservative form, i.e.:
∂C ∂ (uC ) ∂ ( vC ) ∂[( dσ / dt + v f )C ]
+
=
+
+
∂t
∂x
∂y
∂σ
= D x − D y − Dσ − C src + C snk
(14)
is the three-dimensional partial differential one of the parabolic
type. C represents the mass concentration (kg m–3) as defined
by the COAMPS transformed coordinate. The horizontal
velocity components of x and y directions (u and v) and the
particle gravitational fall velocity vf are scaled separately by the
horizontal map scaling factors at the staggered velocity–grid
points and by the σ–coordinate scaling factor
zm = ( ztop − zsfc ) / ztop
(15)
where:
Csrc is the source and Csnk is the sink aerosols or
tracers represented in units of km m–3 s–1.
The source concentration term may represent any of the
following:
•
injection of aerosol particles,
•
formation of new particles by nucleation,
•
tracer emission.
Meso- and microscale models will enhance monitoring of
chemical, biological or radiological contamination threats
resulting from events such as technical damages, catastrophes,
natural disasters or terrorist attacks. The models will also
facilitate creation of possible contamination scenarios ensuring
the ability to identify areas threatened with pollution
concentration. In cases of emergency, sufficient information
about the speed and direction of pollution spreading is critical
to minimize risk to residents of threatened areas as well as to
rescue teams.
The sink concentration term may represent a parameterized
precipitation removal, surface deposition, or other processes
(e.g., heterogeneous nucleation). The terms Dx, Dy, and Dσ all
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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B8. Beijing 2008
represent subgrid scale turbulent mixing in the x, y, and σ
directions. The abovementioned terms are defined as follows:
Dx =
∂ ⎛ ∂C ⎞
∂ ⎛ ∂C ⎞
⎜ Kx
⎟ Dx = ⎜ K x
⎟
∂x ⎝
∂x ⎠
∂x ⎝
∂x ⎠
⎛ z top
Dσ = ⎜
⎜z −z
sfc
⎝ top
where:
σ = z top
(15)
2
⎞ ∂ ⎛
∂C ⎞
⎟
K
⎟ ∂σ ⎜⎝ σ ∂σ ⎟⎠
⎠
(16)
z − z sfc
z top − z sfc
TM
Figure 8. Warsaw Power Plants (Google
It is general vertical coordinate, augmented with the COAMPS
terrain–following sigma coordinate. In the sigma formula, z is
the vertical altitude, ztop is the depth of model domain, and zsfc is
the terrain height at the grid points.
).
3.3 Vertical structure of the COAMPS
z
dsigwaÃ
1Ä
z top
dsigmaÃ
1Ä
wÃ
1Ä
u, v, 6, E
, e, q x Ã
1Ä
dsigwaÃ
2Ä
wÃ
2Ä
dsigmaÃ
2Ä
u, v, 6, E
, e, q x Ã
1Ä
wÃ
3Ä
wÃ
K "1Ä
dsigmaÃ
K "1Ä
u, v, 6, E
, e, q x Ã
K "1Ä
Figure 9. The system for time – spatial analysis.
wÃ
KÄ
dsigmaÃ
KÄ
z
z sfc
, e, q x Ã
KÄ
u, v, 6, E
wÃ
K 1Ä
3.5 Data analysis
The data can be interpolated on the locally parallel surfaces.
Additionally, the presented module can deliver information on
weakening of the stream (extinction factor) and the radiation
optical length. Due to a very large amount of output data, a
dedicated application for analysis (Figure 9) was developed in
the Applied Geomatics Section. The application enables:
•
simultaneous tracing of pollution propagation and
weather changes for different sub-areas of Europe
(functionality for defining calculation grids),
•
analysis of the non-stationary distributions of volume
and surface pollution for every single emitor and a
combined group of emitors,
•
detection of concentration levels exceeding the
allowed ones,
•
measuring the influence of meteorological conditions:
inversion (sedimentation of pollution near the
emitors), convection (long-range transportation),
deposition (dry and wet),
•
uniform data processing system and their registration,
archivization and sharing.
Figure 7. The vertical structure of the COAMPS.
COAMPS includes 30 levels of data, but it is possible to
increase the number of levels by about 10. For the analysis of
the gas pollution spreading the most important layer is the
ground level – 1 600m. In this range we have the following
heights (in [m]):
0.0; 10.0, 20.0, 30.0, 40.0, 55.0, 70.0, 90.0, 110.0, 140.0,
170.0, 215.0, 260.0, 330.0, 400.0, 500.0, 600.0, 750.0, 900.0,
1100.0, 1300.0, 1600.0
3.4 The numerical simulations
The several numerical simulations were carried out on the base
of COAMPS. They include the Warsaw area (Figure 8) and the
Mazovian Province area. The quantities of the emitted pollution
were not taken from reports officially published by the power
plants and steelworks supervisory boards. They were assumed
for the calculations needs only. Authors do not take the
responsibility for publishing by other persons results of tests
presented here.
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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B8. Beijing 2008
3.6 Meteorological conditions
Figure 10.
Vertical motion field over the Mazovian
Province, 29.02.2008 – weak convection, in [m s-1].
Figure 13.
Vertical range of gas pollutions in the strong
convection conditions (18.04.2008). The smoke trail reaches
800m level.
The figures presented above illustrate two meteorological
situations: weak and strong convection. The vertical
distributions of gas pollution emitted by Warsaw Power Plants
are different.
The strong convection shortens the horizontal range of the
propagation process. However, the weak convection causes that
the horizontal range is visibly larger, and the contaminants
concentration decompose on the larger area, too.
REFERENCES
Hodur, R.M., 1997. The Naval Research Laboratory’s Coupled
Ocean/Atmosphere Mesoscale Prediction System (COAMPS).,
Mon. Wea. Rev., 135, pp. 1414–1430.
Winnicki, I., 1995, The ellipticity condition of the Monge –
Ampere equation in the solenoidal model., J. Techn. Phys., 36,
pp. 299 – 315.
Figure 11.
Vertical range of gas pollutions in the weak
convection conditions (29.02.2008). The smoke trail reaches
300m level.
ACKNOWLEDGEMENTS
This study is supported by the Ministry of Science and Higher
Education, Poland: Grant No O N306 0033 33 – Nonhydrostatic mesoscale models data application to
meteorological support of Air Force operations.
Figure 12.
Vertical motion field over the Mazovian
Province, 18.04.2008 – strong convection, in [m s-1].
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